0.9999...=∞(0.9)(0.1)^n-1= 0.9/1-0.1=1,
∑
n=1
using the geometric series. By the same method, compute the exact
value of the following periodic innite decimal expression as a rational number: 0:89898989
First let me rewrite what I think you tried to convey:
If you do long division of 1-0.1 into 0.9 you get the infinite series .9 + .01 + .009 + ....; Hence 0.99999... = 1.
For the number 0.898989.. you have:
.
To show this do the long division of 1 - .01 into 0.89.